#include <iostream>
#include "../../src/FTensor.hpp"
#include "test_for_zero.hpp"
using namespace FTensor;
using namespace std;

void test_T4R()
{
  Index<'i',3> i;
  Index<'j',3> j;
  Index<'k',3> k;
  Index<'l',3> l;
  Index<'m',3> m;
  Index<'n',3> n;

  Number<0> N0;
  Number<1> N1;
  Number<2> N2;

  Tensor4_Riemann<double,3> t4R_1, t4R_2, t4R_3;

  Tensor2_symmetric<double,3> delta_3(3,0,0,3,0,3), delta_5(5,0,0,5,0,5),
    delta_2(2,0,0,2,0,2), delta_7(7,0,0,7,0,7);

  t4R_1(i,j,k,l)=(delta_3(i,k)*delta_5(j,l) && delta_3(i,l)*delta_5(k,j));

  test_for_zero(t4R_1(0,0,0,0) - (delta_3(0,0)*delta_5(0,0)-delta_3(0,0)*delta_5(0,0)),
                "T4ddg && T4ddg (0,0,0,0)");
  test_for_zero(t4R_1(0,0,0,1) - (delta_3(0,1)*delta_5(0,0)-delta_3(0,1)*delta_5(0,0)),
                "T4ddg && T4ddg (0,0,0,1)");
  test_for_zero(t4R_1(0,0,0,2) - (delta_3(0,2)*delta_5(0,0)-delta_3(0,2)*delta_5(0,0)),
                "T4ddg && T4ddg (0,0,0,2)");
  test_for_zero(t4R_1(0,0,1,0) - (delta_3(0,0)*delta_5(0,1)-delta_3(0,0)*delta_5(1,0)),
                "T4ddg && T4ddg (0,0,1,0)");
  test_for_zero(t4R_1(0,0,1,1) - (delta_3(0,1)*delta_5(0,1)-delta_3(0,1)*delta_5(1,0)),
                "T4ddg && T4ddg (0,0,1,1)");
  test_for_zero(t4R_1(0,0,1,2) - (delta_3(0,2)*delta_5(0,1)-delta_3(0,2)*delta_5(1,0)),
                "T4ddg && T4ddg (0,0,1,2)");
  test_for_zero(t4R_1(0,0,2,0) - (delta_3(0,0)*delta_5(0,2)-delta_3(0,0)*delta_5(2,0)),
                "T4ddg && T4ddg (0,0,2,0)");
  test_for_zero(t4R_1(0,0,2,1) - (delta_3(0,1)*delta_5(0,2)-delta_3(0,1)*delta_5(2,0)),
                "T4ddg && T4ddg (0,0,2,1)");
  test_for_zero(t4R_1(0,0,2,2) - (delta_3(0,2)*delta_5(0,2)-delta_3(0,2)*delta_5(2,0)),
                "T4ddg && T4ddg (0,0,2,2)");
  test_for_zero(t4R_1(0,1,0,0) - (delta_3(0,0)*delta_5(1,0)-delta_3(0,0)*delta_5(0,1)),
                "T4ddg && T4ddg (0,1,0,0)");
  test_for_zero(t4R_1(0,1,0,1) - (delta_3(0,0)*delta_5(1,1)-delta_3(0,1)*delta_5(0,1)),
                "T4ddg && T4ddg (0,1,0,1)");
  test_for_zero(t4R_1(0,1,0,2) - (delta_3(0,2)*delta_5(1,0)-delta_3(0,2)*delta_5(0,1)),
                "T4ddg && T4ddg (0,1,0,2)");
  test_for_zero(t4R_1(0,1,1,0) - (delta_3(0,0)*delta_5(1,1)-delta_3(0,0)*delta_5(1,1)),
                "T4ddg && T4ddg (0,1,1,0)");
  test_for_zero(t4R_1(0,1,1,1) - (delta_3(0,1)*delta_5(1,1)-delta_3(0,1)*delta_5(1,1)),
                "T4ddg && T4ddg (0,1,1,1)");
  test_for_zero(t4R_1(0,1,1,2) - (delta_3(0,2)*delta_5(1,1)-delta_3(0,2)*delta_5(1,1)),
                "T4ddg && T4ddg (0,1,1,2)");
  test_for_zero(t4R_1(0,1,2,0) - (delta_3(0,0)*delta_5(1,2)-delta_3(0,0)*delta_5(2,1)),
                "T4ddg && T4ddg (0,1,2,0)");
  test_for_zero(t4R_1(0,1,2,1) - (delta_3(0,1)*delta_5(1,2)-delta_3(0,1)*delta_5(2,1)),
                "T4ddg && T4ddg (0,1,2,1)");
  test_for_zero(t4R_1(0,1,2,2) - (delta_3(0,2)*delta_5(1,2)-delta_3(0,2)*delta_5(2,1)),
                "T4ddg && T4ddg (0,1,2,2)");
  test_for_zero(t4R_1(0,2,0,0) - (delta_3(0,0)*delta_5(2,0)-delta_3(0,0)*delta_5(0,2)),
                "T4ddg && T4ddg (0,2,0,0)");
  test_for_zero(t4R_1(0,2,0,1) - (delta_3(0,1)*delta_5(2,0)-delta_3(0,1)*delta_5(0,2)),
                "T4ddg && T4ddg (0,2,0,1)");
  test_for_zero(t4R_1(0,2,0,2) - (delta_3(0,0)*delta_5(2,2)-delta_3(0,2)*delta_5(0,2)),
                "T4ddg && T4ddg (0,2,0,2)");
  test_for_zero(t4R_1(0,2,1,0) - (delta_3(0,0)*delta_5(2,1)-delta_3(0,0)*delta_5(1,2)),
                "T4ddg && T4ddg (0,2,1,0)");
  test_for_zero(t4R_1(0,2,1,1) - (delta_3(0,1)*delta_5(2,1)-delta_3(0,1)*delta_5(1,2)),
                "T4ddg && T4ddg (0,2,1,1)");
  test_for_zero(t4R_1(0,2,1,2) - (delta_3(0,2)*delta_5(2,1)-delta_3(0,2)*delta_5(1,2)),
                "T4ddg && T4ddg (0,2,1,2)");
  test_for_zero(t4R_1(0,2,2,0) - (delta_3(0,0)*delta_5(2,2)-delta_3(0,0)*delta_5(2,2)),
                "T4ddg && T4ddg (0,2,2,0)");
  test_for_zero(t4R_1(0,2,2,1) - (delta_3(0,1)*delta_5(2,2)-delta_3(0,1)*delta_5(2,2)),
                "T4ddg && T4ddg (0,2,2,1)");
  test_for_zero(t4R_1(0,2,2,2) - (delta_3(0,2)*delta_5(2,2)-delta_3(0,2)*delta_5(2,2)),
                "T4ddg && T4ddg (0,2,2,2)");
  test_for_zero(t4R_1(1,0,0,0) - (delta_3(1,0)*delta_5(0,0)-delta_3(1,0)*delta_5(0,0)),
                "T4ddg && T4ddg (1,0,0,0)");
  test_for_zero(t4R_1(1,0,0,1) - (delta_3(1,1)*delta_5(0,0)-delta_3(1,1)*delta_5(0,0)),
                "T4ddg && T4ddg (1,0,0,1)");
  test_for_zero(t4R_1(1,0,0,2) - (delta_3(1,2)*delta_5(0,0)-delta_3(1,2)*delta_5(0,0)),
                "T4ddg && T4ddg (1,0,0,2)");
  test_for_zero(t4R_1(1,0,1,0) - (delta_3(1,0)*delta_5(0,1)-delta_3(1,0)*delta_5(1,0)),
                "T4ddg && T4ddg (1,0,1,0)");
  test_for_zero(t4R_1(1,0,1,1) - (delta_3(1,1)*delta_5(0,1)-delta_3(1,1)*delta_5(1,0)),
                "T4ddg && T4ddg (1,0,1,1)");
  test_for_zero(t4R_1(1,0,1,2) - (delta_3(1,2)*delta_5(0,1)-delta_3(1,2)*delta_5(1,0)),
                "T4ddg && T4ddg (1,0,1,2)");
  test_for_zero(t4R_1(1,0,2,0) - (delta_3(1,0)*delta_5(0,2)-delta_3(1,0)*delta_5(2,0)),
                "T4ddg && T4ddg (1,0,2,0)");
  test_for_zero(t4R_1(1,0,2,1) - (delta_3(1,1)*delta_5(0,2)-delta_3(1,1)*delta_5(2,0)),
                "T4ddg && T4ddg (1,0,2,1)");
  test_for_zero(t4R_1(1,0,2,2) - (delta_3(1,2)*delta_5(0,2)-delta_3(1,2)*delta_5(2,0)),
                "T4ddg && T4ddg (1,0,2,2)");
  test_for_zero(t4R_1(1,1,0,0) - (delta_3(1,0)*delta_5(1,0)-delta_3(1,0)*delta_5(0,1)),
                "T4ddg && T4ddg (1,1,0,0)");
  test_for_zero(t4R_1(1,1,0,1) - (delta_3(1,1)*delta_5(1,0)-delta_3(1,1)*delta_5(0,1)),
                "T4ddg && T4ddg (1,1,0,1)");
  test_for_zero(t4R_1(1,1,0,2) - (delta_3(1,2)*delta_5(1,0)-delta_3(1,2)*delta_5(0,1)),
                "T4ddg && T4ddg (1,1,0,2)");
  test_for_zero(t4R_1(1,1,1,0) - (delta_3(1,0)*delta_5(1,1)-delta_3(1,0)*delta_5(1,1)),
                "T4ddg && T4ddg (1,1,1,0)");
  test_for_zero(t4R_1(1,1,1,1) - (delta_3(1,1)*delta_5(1,1)-delta_3(1,1)*delta_5(1,1)),
                "T4ddg && T4ddg (1,1,1,1)");
  test_for_zero(t4R_1(1,1,1,2) - (delta_3(1,2)*delta_5(1,1)-delta_3(1,2)*delta_5(1,1)),
                "T4ddg && T4ddg (1,1,1,2)");
  test_for_zero(t4R_1(1,1,2,0) - (delta_3(1,0)*delta_5(1,2)-delta_3(1,0)*delta_5(2,1)),
                "T4ddg && T4ddg (1,1,2,0)");
  test_for_zero(t4R_1(1,1,2,1) - (delta_3(1,1)*delta_5(1,2)-delta_3(1,1)*delta_5(2,1)),
                "T4ddg && T4ddg (1,1,2,1)");
  test_for_zero(t4R_1(1,1,2,2) - (delta_3(1,2)*delta_5(1,2)-delta_3(1,2)*delta_5(2,1)),
                "T4ddg && T4ddg (1,1,2,2)");
  test_for_zero(t4R_1(1,2,0,0) - (delta_3(1,0)*delta_5(2,0)-delta_3(1,0)*delta_5(0,2)),
                "T4ddg && T4ddg (1,2,0,0)");
  test_for_zero(t4R_1(1,2,0,1) - (delta_3(1,1)*delta_5(2,0)-delta_3(1,1)*delta_5(0,2)),
                "T4ddg && T4ddg (1,2,0,1)");
  test_for_zero(t4R_1(1,2,0,2) - (delta_3(1,2)*delta_5(2,0)-delta_3(1,2)*delta_5(0,2)),
                "T4ddg && T4ddg (1,2,0,2)");
  test_for_zero(t4R_1(1,2,1,0) - (delta_3(1,0)*delta_5(2,1)-delta_3(1,0)*delta_5(1,2)),
                "T4ddg && T4ddg (1,2,1,0)");
  test_for_zero(t4R_1(1,2,1,1) - (delta_3(1,1)*delta_5(2,1)-delta_3(1,1)*delta_5(1,2)),
                "T4ddg && T4ddg (1,2,1,1)");
  test_for_zero(t4R_1(1,2,1,2) - (delta_3(1,1)*delta_5(2,2)-delta_3(1,2)*delta_5(1,2)),
                "T4ddg && T4ddg (1,2,1,2)");
  test_for_zero(t4R_1(1,2,2,0) - (delta_3(1,0)*delta_5(2,2)-delta_3(1,0)*delta_5(2,2)),
                "T4ddg && T4ddg (1,2,2,0)");
  test_for_zero(t4R_1(1,2,2,1) - (delta_3(1,1)*delta_5(2,2)-delta_3(1,1)*delta_5(2,2)),
                "T4ddg && T4ddg (1,2,2,1)");
  test_for_zero(t4R_1(1,2,2,2) - (delta_3(1,2)*delta_5(2,2)-delta_3(1,2)*delta_5(2,2)),
                "T4ddg && T4ddg (1,2,2,2)");
  test_for_zero(t4R_1(2,0,0,0) - (delta_3(2,0)*delta_5(0,0)-delta_3(2,0)*delta_5(0,0)),
                "T4ddg && T4ddg (2,0,0,0)");
  test_for_zero(t4R_1(2,0,0,1) - (delta_3(2,1)*delta_5(0,0)-delta_3(2,1)*delta_5(0,0)),
                "T4ddg && T4ddg (2,0,0,1)");
  test_for_zero(t4R_1(2,0,0,2) - (delta_3(2,2)*delta_5(0,0)-delta_3(2,2)*delta_5(0,0)),
                "T4ddg && T4ddg (2,0,0,2)");
  test_for_zero(t4R_1(2,0,1,0) - (delta_3(2,0)*delta_5(0,1)-delta_3(2,0)*delta_5(1,0)),
                "T4ddg && T4ddg (2,0,1,0)");
  test_for_zero(t4R_1(2,0,1,1) - (delta_3(2,1)*delta_5(0,1)-delta_3(2,1)*delta_5(1,0)),
                "T4ddg && T4ddg (2,0,1,1)");
  test_for_zero(t4R_1(2,0,1,2) - (delta_3(2,2)*delta_5(0,1)-delta_3(2,2)*delta_5(1,0)),
                "T4ddg && T4ddg (2,0,1,2)");
  test_for_zero(t4R_1(2,0,2,0) - (delta_3(2,0)*delta_5(0,2)-delta_3(2,0)*delta_5(2,0)),
                "T4ddg && T4ddg (2,0,2,0)");
  test_for_zero(t4R_1(2,0,2,1) - (delta_3(2,1)*delta_5(0,2)-delta_3(2,1)*delta_5(2,0)),
                "T4ddg && T4ddg (2,0,2,1)");
  test_for_zero(t4R_1(2,0,2,2) - (delta_3(2,2)*delta_5(0,2)-delta_3(2,2)*delta_5(2,0)),
                "T4ddg && T4ddg (2,0,2,2)");
  test_for_zero(t4R_1(2,1,0,0) - (delta_3(2,0)*delta_5(1,0)-delta_3(2,0)*delta_5(0,1)),
                "T4ddg && T4ddg (2,1,0,0)");
  test_for_zero(t4R_1(2,1,0,1) - (delta_3(2,1)*delta_5(1,0)-delta_3(2,1)*delta_5(0,1)),
                "T4ddg && T4ddg (2,1,0,1)");
  test_for_zero(t4R_1(2,1,0,2) - (delta_3(2,2)*delta_5(1,0)-delta_3(2,2)*delta_5(0,1)),
                "T4ddg && T4ddg (2,1,0,2)");
  test_for_zero(t4R_1(2,1,1,0) - (delta_3(2,0)*delta_5(1,1)-delta_3(2,0)*delta_5(1,1)),
                "T4ddg && T4ddg (2,1,1,0)");
  test_for_zero(t4R_1(2,1,1,1) - (delta_3(2,1)*delta_5(1,1)-delta_3(2,1)*delta_5(1,1)),
                "T4ddg && T4ddg (2,1,1,1)");
  test_for_zero(t4R_1(2,1,1,2) - (delta_3(2,2)*delta_5(1,1)-delta_3(2,2)*delta_5(1,1)),
                "T4ddg && T4ddg (2,1,1,2)");
  test_for_zero(t4R_1(2,1,2,0) - (delta_3(2,0)*delta_5(1,2)-delta_3(2,0)*delta_5(2,1)),
                "T4ddg && T4ddg (2,1,2,0)");
  test_for_zero(t4R_1(2,1,2,1) - (delta_3(2,1)*delta_5(1,2)-delta_3(2,1)*delta_5(2,1)),
                "T4ddg && T4ddg (2,1,2,1)");
  test_for_zero(t4R_1(2,1,2,2) - (delta_3(2,2)*delta_5(1,2)-delta_3(2,2)*delta_5(2,1)),
                "T4ddg && T4ddg (2,1,2,2)");
  test_for_zero(t4R_1(2,2,0,0) - (delta_3(2,0)*delta_5(2,0)-delta_3(2,0)*delta_5(0,2)),
                "T4ddg && T4ddg (2,2,0,0)");
  test_for_zero(t4R_1(2,2,0,1) - (delta_3(2,1)*delta_5(2,0)-delta_3(2,1)*delta_5(0,2)),
                "T4ddg && T4ddg (2,2,0,1)");
  test_for_zero(t4R_1(2,2,0,2) - (delta_3(2,2)*delta_5(2,0)-delta_3(2,2)*delta_5(0,2)),
                "T4ddg && T4ddg (2,2,0,2)");
  test_for_zero(t4R_1(2,2,1,0) - (delta_3(2,0)*delta_5(2,1)-delta_3(2,0)*delta_5(1,2)),
                "T4ddg && T4ddg (2,2,1,0)");
  test_for_zero(t4R_1(2,2,1,1) - (delta_3(2,1)*delta_5(2,1)-delta_3(2,1)*delta_5(1,2)),
                "T4ddg && T4ddg (2,2,1,1)");
  test_for_zero(t4R_1(2,2,1,2) - (delta_3(2,2)*delta_5(2,1)-delta_3(2,2)*delta_5(1,2)),
                "T4ddg && T4ddg (2,2,1,2)");
  test_for_zero(t4R_1(2,2,2,0) - (delta_3(2,0)*delta_5(2,2)-delta_3(2,0)*delta_5(2,2)),
                "T4ddg && T4ddg (2,2,2,0)");
  test_for_zero(t4R_1(2,2,2,1) - (delta_3(2,1)*delta_5(2,2)-delta_3(2,1)*delta_5(2,2)),
                "T4ddg && T4ddg (2,2,2,1)");
  test_for_zero(t4R_1(2,2,2,2) - (delta_3(2,2)*delta_5(2,2)-delta_3(2,2)*delta_5(2,2)),
                "T4ddg && T4ddg (2,2,2,2)");


  t4R_2(i,j,k,l)=(delta_2(i,k)*delta_7(j,l) && delta_2(i,l)*delta_7(k,j));

  t4R_3(i,j,k,l)=t4R_1(i,j,k,l)+t4R_2(i,j,k,l);
  test_for_zero(t4R_3(0,0,0,0) - (t4R_1(0,0,0,0)+t4R_2(0,0,0,0)),
                "T4R + T4R (0,0,0,0)");
  test_for_zero(t4R_3(0,0,0,1) - (t4R_1(0,0,0,1)+t4R_2(0,0,0,1)),
                "T4R + T4R (0,0,0,1)");
  test_for_zero(t4R_3(0,0,0,2) - (t4R_1(0,0,0,2)+t4R_2(0,0,0,2)),
                "T4R + T4R (0,0,0,2)");
  test_for_zero(t4R_3(0,0,1,0) - (t4R_1(0,0,1,0)+t4R_2(0,0,1,0)),
                "T4R + T4R (0,0,1,0)");
  test_for_zero(t4R_3(0,0,1,1) - (t4R_1(0,0,1,1)+t4R_2(0,0,1,1)),
                "T4R + T4R (0,0,1,1)");
  test_for_zero(t4R_3(0,0,1,2) - (t4R_1(0,0,1,2)+t4R_2(0,0,1,2)),
                "T4R + T4R (0,0,1,2)");
  test_for_zero(t4R_3(0,0,2,0) - (t4R_1(0,0,2,0)+t4R_2(0,0,2,0)),
                "T4R + T4R (0,0,2,0)");
  test_for_zero(t4R_3(0,0,2,1) - (t4R_1(0,0,2,1)+t4R_2(0,0,2,1)),
                "T4R + T4R (0,0,2,1)");
  test_for_zero(t4R_3(0,0,2,2) - (t4R_1(0,0,2,2)+t4R_2(0,0,2,2)),
                "T4R + T4R (0,0,2,2)");
  test_for_zero(t4R_3(0,1,0,0) - (t4R_1(0,1,0,0)+t4R_2(0,1,0,0)),
                "T4R + T4R (0,1,0,0)");
  test_for_zero(t4R_3(0,1,0,1) - (t4R_1(0,1,0,1)+t4R_2(0,1,0,1)),
                "T4R + T4R (0,1,0,1)");
  test_for_zero(t4R_3(0,1,0,2) - (t4R_1(0,1,0,2)+t4R_2(0,1,0,2)),
                "T4R + T4R (0,1,0,2)");
  test_for_zero(t4R_3(0,1,1,0) - (t4R_1(0,1,1,0)+t4R_2(0,1,1,0)),
                "T4R + T4R (0,1,1,0)");
  test_for_zero(t4R_3(0,1,1,1) - (t4R_1(0,1,1,1)+t4R_2(0,1,1,1)),
                "T4R + T4R (0,1,1,1)");
  test_for_zero(t4R_3(0,1,1,2) - (t4R_1(0,1,1,2)+t4R_2(0,1,1,2)),
                "T4R + T4R (0,1,1,2)");
  test_for_zero(t4R_3(0,1,2,0) - (t4R_1(0,1,2,0)+t4R_2(0,1,2,0)),
                "T4R + T4R (0,1,2,0)");
  test_for_zero(t4R_3(0,1,2,1) - (t4R_1(0,1,2,1)+t4R_2(0,1,2,1)),
                "T4R + T4R (0,1,2,1)");
  test_for_zero(t4R_3(0,1,2,2) - (t4R_1(0,1,2,2)+t4R_2(0,1,2,2)),
                "T4R + T4R (0,1,2,2)");
  test_for_zero(t4R_3(0,2,0,0) - (t4R_1(0,2,0,0)+t4R_2(0,2,0,0)),
                "T4R + T4R (0,2,0,0)");
  test_for_zero(t4R_3(0,2,0,1) - (t4R_1(0,2,0,1)+t4R_2(0,2,0,1)),
                "T4R + T4R (0,2,0,1)");
  test_for_zero(t4R_3(0,2,0,2) - (t4R_1(0,2,0,2)+t4R_2(0,2,0,2)),
                "T4R + T4R (0,2,0,2)");
  test_for_zero(t4R_3(0,2,1,0) - (t4R_1(0,2,1,0)+t4R_2(0,2,1,0)),
                "T4R + T4R (0,2,1,0)");
  test_for_zero(t4R_3(0,2,1,1) - (t4R_1(0,2,1,1)+t4R_2(0,2,1,1)),
                "T4R + T4R (0,2,1,1)");
  test_for_zero(t4R_3(0,2,1,2) - (t4R_1(0,2,1,2)+t4R_2(0,2,1,2)),
                "T4R + T4R (0,2,1,2)");
  test_for_zero(t4R_3(0,2,2,0) - (t4R_1(0,2,2,0)+t4R_2(0,2,2,0)),
                "T4R + T4R (0,2,2,0)");
  test_for_zero(t4R_3(0,2,2,1) - (t4R_1(0,2,2,1)+t4R_2(0,2,2,1)),
                "T4R + T4R (0,2,2,1)");
  test_for_zero(t4R_3(0,2,2,2) - (t4R_1(0,2,2,2)+t4R_2(0,2,2,2)),
                "T4R + T4R (0,2,2,2)");
  test_for_zero(t4R_3(1,0,0,0) - (t4R_1(1,0,0,0)+t4R_2(1,0,0,0)),
                "T4R + T4R (1,0,0,0)");
  test_for_zero(t4R_3(1,0,0,1) - (t4R_1(1,0,0,1)+t4R_2(1,0,0,1)),
                "T4R + T4R (1,0,0,1)");
  test_for_zero(t4R_3(1,0,0,2) - (t4R_1(1,0,0,2)+t4R_2(1,0,0,2)),
                "T4R + T4R (1,0,0,2)");
  test_for_zero(t4R_3(1,0,1,0) - (t4R_1(1,0,1,0)+t4R_2(1,0,1,0)),
                "T4R + T4R (1,0,1,0)");
  test_for_zero(t4R_3(1,0,1,1) - (t4R_1(1,0,1,1)+t4R_2(1,0,1,1)),
                "T4R + T4R (1,0,1,1)");
  test_for_zero(t4R_3(1,0,1,2) - (t4R_1(1,0,1,2)+t4R_2(1,0,1,2)),
                "T4R + T4R (1,0,1,2)");
  test_for_zero(t4R_3(1,0,2,0) - (t4R_1(1,0,2,0)+t4R_2(1,0,2,0)),
                "T4R + T4R (1,0,2,0)");
  test_for_zero(t4R_3(1,0,2,1) - (t4R_1(1,0,2,1)+t4R_2(1,0,2,1)),
                "T4R + T4R (1,0,2,1)");
  test_for_zero(t4R_3(1,0,2,2) - (t4R_1(1,0,2,2)+t4R_2(1,0,2,2)),
                "T4R + T4R (1,0,2,2)");
  test_for_zero(t4R_3(1,1,0,0) - (t4R_1(1,1,0,0)+t4R_2(1,1,0,0)),
                "T4R + T4R (1,1,0,0)");
  test_for_zero(t4R_3(1,1,0,1) - (t4R_1(1,1,0,1)+t4R_2(1,1,0,1)),
                "T4R + T4R (1,1,0,1)");
  test_for_zero(t4R_3(1,1,0,2) - (t4R_1(1,1,0,2)+t4R_2(1,1,0,2)),
                "T4R + T4R (1,1,0,2)");
  test_for_zero(t4R_3(1,1,1,0) - (t4R_1(1,1,1,0)+t4R_2(1,1,1,0)),
                "T4R + T4R (1,1,1,0)");
  test_for_zero(t4R_3(1,1,1,1) - (t4R_1(1,1,1,1)+t4R_2(1,1,1,1)),
                "T4R + T4R (1,1,1,1)");
  test_for_zero(t4R_3(1,1,1,2) - (t4R_1(1,1,1,2)+t4R_2(1,1,1,2)),
                "T4R + T4R (1,1,1,2)");
  test_for_zero(t4R_3(1,1,2,0) - (t4R_1(1,1,2,0)+t4R_2(1,1,2,0)),
                "T4R + T4R (1,1,2,0)");
  test_for_zero(t4R_3(1,1,2,1) - (t4R_1(1,1,2,1)+t4R_2(1,1,2,1)),
                "T4R + T4R (1,1,2,1)");
  test_for_zero(t4R_3(1,1,2,2) - (t4R_1(1,1,2,2)+t4R_2(1,1,2,2)),
                "T4R + T4R (1,1,2,2)");
  test_for_zero(t4R_3(1,2,0,0) - (t4R_1(1,2,0,0)+t4R_2(1,2,0,0)),
                "T4R + T4R (1,2,0,0)");
  test_for_zero(t4R_3(1,2,0,1) - (t4R_1(1,2,0,1)+t4R_2(1,2,0,1)),
                "T4R + T4R (1,2,0,1)");
  test_for_zero(t4R_3(1,2,0,2) - (t4R_1(1,2,0,2)+t4R_2(1,2,0,2)),
                "T4R + T4R (1,2,0,2)");
  test_for_zero(t4R_3(1,2,1,0) - (t4R_1(1,2,1,0)+t4R_2(1,2,1,0)),
                "T4R + T4R (1,2,1,0)");
  test_for_zero(t4R_3(1,2,1,1) - (t4R_1(1,2,1,1)+t4R_2(1,2,1,1)),
                "T4R + T4R (1,2,1,1)");
  test_for_zero(t4R_3(1,2,1,2) - (t4R_1(1,2,1,2)+t4R_2(1,2,1,2)),
                "T4R + T4R (1,2,1,2)");
  test_for_zero(t4R_3(1,2,2,0) - (t4R_1(1,2,2,0)+t4R_2(1,2,2,0)),
                "T4R + T4R (1,2,2,0)");
  test_for_zero(t4R_3(1,2,2,1) - (t4R_1(1,2,2,1)+t4R_2(1,2,2,1)),
                "T4R + T4R (1,2,2,1)");
  test_for_zero(t4R_3(1,2,2,2) - (t4R_1(1,2,2,2)+t4R_2(1,2,2,2)),
                "T4R + T4R (1,2,2,2)");
  test_for_zero(t4R_3(2,0,0,0) - (t4R_1(2,0,0,0)+t4R_2(2,0,0,0)),
                "T4R + T4R (2,0,0,0)");
  test_for_zero(t4R_3(2,0,0,1) - (t4R_1(2,0,0,1)+t4R_2(2,0,0,1)),
                "T4R + T4R (2,0,0,1)");
  test_for_zero(t4R_3(2,0,0,2) - (t4R_1(2,0,0,2)+t4R_2(2,0,0,2)),
                "T4R + T4R (2,0,0,2)");
  test_for_zero(t4R_3(2,0,1,0) - (t4R_1(2,0,1,0)+t4R_2(2,0,1,0)),
                "T4R + T4R (2,0,1,0)");
  test_for_zero(t4R_3(2,0,1,1) - (t4R_1(2,0,1,1)+t4R_2(2,0,1,1)),
                "T4R + T4R (2,0,1,1)");
  test_for_zero(t4R_3(2,0,1,2) - (t4R_1(2,0,1,2)+t4R_2(2,0,1,2)),
                "T4R + T4R (2,0,1,2)");
  test_for_zero(t4R_3(2,0,2,0) - (t4R_1(2,0,2,0)+t4R_2(2,0,2,0)),
                "T4R + T4R (2,0,2,0)");
  test_for_zero(t4R_3(2,0,2,1) - (t4R_1(2,0,2,1)+t4R_2(2,0,2,1)),
                "T4R + T4R (2,0,2,1)");
  test_for_zero(t4R_3(2,0,2,2) - (t4R_1(2,0,2,2)+t4R_2(2,0,2,2)),
                "T4R + T4R (2,0,2,2)");
  test_for_zero(t4R_3(2,1,0,0) - (t4R_1(2,1,0,0)+t4R_2(2,1,0,0)),
                "T4R + T4R (2,1,0,0)");
  test_for_zero(t4R_3(2,1,0,1) - (t4R_1(2,1,0,1)+t4R_2(2,1,0,1)),
                "T4R + T4R (2,1,0,1)");
  test_for_zero(t4R_3(2,1,0,2) - (t4R_1(2,1,0,2)+t4R_2(2,1,0,2)),
                "T4R + T4R (2,1,0,2)");
  test_for_zero(t4R_3(2,1,1,0) - (t4R_1(2,1,1,0)+t4R_2(2,1,1,0)),
                "T4R + T4R (2,1,1,0)");
  test_for_zero(t4R_3(2,1,1,1) - (t4R_1(2,1,1,1)+t4R_2(2,1,1,1)),
                "T4R + T4R (2,1,1,1)");
  test_for_zero(t4R_3(2,1,1,2) - (t4R_1(2,1,1,2)+t4R_2(2,1,1,2)),
                "T4R + T4R (2,1,1,2)");
  test_for_zero(t4R_3(2,1,2,0) - (t4R_1(2,1,2,0)+t4R_2(2,1,2,0)),
                "T4R + T4R (2,1,2,0)");
  test_for_zero(t4R_3(2,1,2,1) - (t4R_1(2,1,2,1)+t4R_2(2,1,2,1)),
                "T4R + T4R (2,1,2,1)");
  test_for_zero(t4R_3(2,1,2,2) - (t4R_1(2,1,2,2)+t4R_2(2,1,2,2)),
                "T4R + T4R (2,1,2,2)");
  test_for_zero(t4R_3(2,2,0,0) - (t4R_1(2,2,0,0)+t4R_2(2,2,0,0)),
                "T4R + T4R (2,2,0,0)");
  test_for_zero(t4R_3(2,2,0,1) - (t4R_1(2,2,0,1)+t4R_2(2,2,0,1)),
                "T4R + T4R (2,2,0,1)");
  test_for_zero(t4R_3(2,2,0,2) - (t4R_1(2,2,0,2)+t4R_2(2,2,0,2)),
                "T4R + T4R (2,2,0,2)");
  test_for_zero(t4R_3(2,2,1,0) - (t4R_1(2,2,1,0)+t4R_2(2,2,1,0)),
                "T4R + T4R (2,2,1,0)");
  test_for_zero(t4R_3(2,2,1,1) - (t4R_1(2,2,1,1)+t4R_2(2,2,1,1)),
                "T4R + T4R (2,2,1,1)");
  test_for_zero(t4R_3(2,2,1,2) - (t4R_1(2,2,1,2)+t4R_2(2,2,1,2)),
                "T4R + T4R (2,2,1,2)");
  test_for_zero(t4R_3(2,2,2,0) - (t4R_1(2,2,2,0)+t4R_2(2,2,2,0)),
                "T4R + T4R (2,2,2,0)");
  test_for_zero(t4R_3(2,2,2,1) - (t4R_1(2,2,2,1)+t4R_2(2,2,2,1)),
                "T4R + T4R (2,2,2,1)");
  test_for_zero(t4R_3(2,2,2,2) - (t4R_1(2,2,2,2)+t4R_2(2,2,2,2)),
                "T4R + T4R (2,2,2,2)");

  t4R_3(i,j,k,l)=t4R_1(i,j,k,l)-t4R_2(i,j,k,l);
  test_for_zero(t4R_3(0,0,0,0) - (t4R_1(0,0,0,0)-t4R_2(0,0,0,0)),
                "T4R - T4R (0,0,0,0)");
  test_for_zero(t4R_3(0,0,0,1) - (t4R_1(0,0,0,1)-t4R_2(0,0,0,1)),
                "T4R - T4R (0,0,0,1)");
  test_for_zero(t4R_3(0,0,0,2) - (t4R_1(0,0,0,2)-t4R_2(0,0,0,2)),
                "T4R - T4R (0,0,0,2)");
  test_for_zero(t4R_3(0,0,1,0) - (t4R_1(0,0,1,0)-t4R_2(0,0,1,0)),
                "T4R - T4R (0,0,1,0)");
  test_for_zero(t4R_3(0,0,1,1) - (t4R_1(0,0,1,1)-t4R_2(0,0,1,1)),
                "T4R - T4R (0,0,1,1)");
  test_for_zero(t4R_3(0,0,1,2) - (t4R_1(0,0,1,2)-t4R_2(0,0,1,2)),
                "T4R - T4R (0,0,1,2)");
  test_for_zero(t4R_3(0,0,2,0) - (t4R_1(0,0,2,0)-t4R_2(0,0,2,0)),
                "T4R - T4R (0,0,2,0)");
  test_for_zero(t4R_3(0,0,2,1) - (t4R_1(0,0,2,1)-t4R_2(0,0,2,1)),
                "T4R - T4R (0,0,2,1)");
  test_for_zero(t4R_3(0,0,2,2) - (t4R_1(0,0,2,2)-t4R_2(0,0,2,2)),
                "T4R - T4R (0,0,2,2)");
  test_for_zero(t4R_3(0,1,0,0) - (t4R_1(0,1,0,0)-t4R_2(0,1,0,0)),
                "T4R - T4R (0,1,0,0)");
  test_for_zero(t4R_3(0,1,0,1) - (t4R_1(0,1,0,1)-t4R_2(0,1,0,1)),
                "T4R - T4R (0,1,0,1)");
  test_for_zero(t4R_3(0,1,0,2) - (t4R_1(0,1,0,2)-t4R_2(0,1,0,2)),
                "T4R - T4R (0,1,0,2)");
  test_for_zero(t4R_3(0,1,1,0) - (t4R_1(0,1,1,0)-t4R_2(0,1,1,0)),
                "T4R - T4R (0,1,1,0)");
  test_for_zero(t4R_3(0,1,1,1) - (t4R_1(0,1,1,1)-t4R_2(0,1,1,1)),
                "T4R - T4R (0,1,1,1)");
  test_for_zero(t4R_3(0,1,1,2) - (t4R_1(0,1,1,2)-t4R_2(0,1,1,2)),
                "T4R - T4R (0,1,1,2)");
  test_for_zero(t4R_3(0,1,2,0) - (t4R_1(0,1,2,0)-t4R_2(0,1,2,0)),
                "T4R - T4R (0,1,2,0)");
  test_for_zero(t4R_3(0,1,2,1) - (t4R_1(0,1,2,1)-t4R_2(0,1,2,1)),
                "T4R - T4R (0,1,2,1)");
  test_for_zero(t4R_3(0,1,2,2) - (t4R_1(0,1,2,2)-t4R_2(0,1,2,2)),
                "T4R - T4R (0,1,2,2)");
  test_for_zero(t4R_3(0,2,0,0) - (t4R_1(0,2,0,0)-t4R_2(0,2,0,0)),
                "T4R - T4R (0,2,0,0)");
  test_for_zero(t4R_3(0,2,0,1) - (t4R_1(0,2,0,1)-t4R_2(0,2,0,1)),
                "T4R - T4R (0,2,0,1)");
  test_for_zero(t4R_3(0,2,0,2) - (t4R_1(0,2,0,2)-t4R_2(0,2,0,2)),
                "T4R - T4R (0,2,0,2)");
  test_for_zero(t4R_3(0,2,1,0) - (t4R_1(0,2,1,0)-t4R_2(0,2,1,0)),
                "T4R - T4R (0,2,1,0)");
  test_for_zero(t4R_3(0,2,1,1) - (t4R_1(0,2,1,1)-t4R_2(0,2,1,1)),
                "T4R - T4R (0,2,1,1)");
  test_for_zero(t4R_3(0,2,1,2) - (t4R_1(0,2,1,2)-t4R_2(0,2,1,2)),
                "T4R - T4R (0,2,1,2)");
  test_for_zero(t4R_3(0,2,2,0) - (t4R_1(0,2,2,0)-t4R_2(0,2,2,0)),
                "T4R - T4R (0,2,2,0)");
  test_for_zero(t4R_3(0,2,2,1) - (t4R_1(0,2,2,1)-t4R_2(0,2,2,1)),
                "T4R - T4R (0,2,2,1)");
  test_for_zero(t4R_3(0,2,2,2) - (t4R_1(0,2,2,2)-t4R_2(0,2,2,2)),
                "T4R - T4R (0,2,2,2)");
  test_for_zero(t4R_3(1,0,0,0) - (t4R_1(1,0,0,0)-t4R_2(1,0,0,0)),
                "T4R - T4R (1,0,0,0)");
  test_for_zero(t4R_3(1,0,0,1) - (t4R_1(1,0,0,1)-t4R_2(1,0,0,1)),
                "T4R - T4R (1,0,0,1)");
  test_for_zero(t4R_3(1,0,0,2) - (t4R_1(1,0,0,2)-t4R_2(1,0,0,2)),
                "T4R - T4R (1,0,0,2)");
  test_for_zero(t4R_3(1,0,1,0) - (t4R_1(1,0,1,0)-t4R_2(1,0,1,0)),
                "T4R - T4R (1,0,1,0)");
  test_for_zero(t4R_3(1,0,1,1) - (t4R_1(1,0,1,1)-t4R_2(1,0,1,1)),
                "T4R - T4R (1,0,1,1)");
  test_for_zero(t4R_3(1,0,1,2) - (t4R_1(1,0,1,2)-t4R_2(1,0,1,2)),
                "T4R - T4R (1,0,1,2)");
  test_for_zero(t4R_3(1,0,2,0) - (t4R_1(1,0,2,0)-t4R_2(1,0,2,0)),
                "T4R - T4R (1,0,2,0)");
  test_for_zero(t4R_3(1,0,2,1) - (t4R_1(1,0,2,1)-t4R_2(1,0,2,1)),
                "T4R - T4R (1,0,2,1)");
  test_for_zero(t4R_3(1,0,2,2) - (t4R_1(1,0,2,2)-t4R_2(1,0,2,2)),
                "T4R - T4R (1,0,2,2)");
  test_for_zero(t4R_3(1,1,0,0) - (t4R_1(1,1,0,0)-t4R_2(1,1,0,0)),
                "T4R - T4R (1,1,0,0)");
  test_for_zero(t4R_3(1,1,0,1) - (t4R_1(1,1,0,1)-t4R_2(1,1,0,1)),
                "T4R - T4R (1,1,0,1)");
  test_for_zero(t4R_3(1,1,0,2) - (t4R_1(1,1,0,2)-t4R_2(1,1,0,2)),
                "T4R - T4R (1,1,0,2)");
  test_for_zero(t4R_3(1,1,1,0) - (t4R_1(1,1,1,0)-t4R_2(1,1,1,0)),
                "T4R - T4R (1,1,1,0)");
  test_for_zero(t4R_3(1,1,1,1) - (t4R_1(1,1,1,1)-t4R_2(1,1,1,1)),
                "T4R - T4R (1,1,1,1)");
  test_for_zero(t4R_3(1,1,1,2) - (t4R_1(1,1,1,2)-t4R_2(1,1,1,2)),
                "T4R - T4R (1,1,1,2)");
  test_for_zero(t4R_3(1,1,2,0) - (t4R_1(1,1,2,0)-t4R_2(1,1,2,0)),
                "T4R - T4R (1,1,2,0)");
  test_for_zero(t4R_3(1,1,2,1) - (t4R_1(1,1,2,1)-t4R_2(1,1,2,1)),
                "T4R - T4R (1,1,2,1)");
  test_for_zero(t4R_3(1,1,2,2) - (t4R_1(1,1,2,2)-t4R_2(1,1,2,2)),
                "T4R - T4R (1,1,2,2)");
  test_for_zero(t4R_3(1,2,0,0) - (t4R_1(1,2,0,0)-t4R_2(1,2,0,0)),
                "T4R - T4R (1,2,0,0)");
  test_for_zero(t4R_3(1,2,0,1) - (t4R_1(1,2,0,1)-t4R_2(1,2,0,1)),
                "T4R - T4R (1,2,0,1)");
  test_for_zero(t4R_3(1,2,0,2) - (t4R_1(1,2,0,2)-t4R_2(1,2,0,2)),
                "T4R - T4R (1,2,0,2)");
  test_for_zero(t4R_3(1,2,1,0) - (t4R_1(1,2,1,0)-t4R_2(1,2,1,0)),
                "T4R - T4R (1,2,1,0)");
  test_for_zero(t4R_3(1,2,1,1) - (t4R_1(1,2,1,1)-t4R_2(1,2,1,1)),
                "T4R - T4R (1,2,1,1)");
  test_for_zero(t4R_3(1,2,1,2) - (t4R_1(1,2,1,2)-t4R_2(1,2,1,2)),
                "T4R - T4R (1,2,1,2)");
  test_for_zero(t4R_3(1,2,2,0) - (t4R_1(1,2,2,0)-t4R_2(1,2,2,0)),
                "T4R - T4R (1,2,2,0)");
  test_for_zero(t4R_3(1,2,2,1) - (t4R_1(1,2,2,1)-t4R_2(1,2,2,1)),
                "T4R - T4R (1,2,2,1)");
  test_for_zero(t4R_3(1,2,2,2) - (t4R_1(1,2,2,2)-t4R_2(1,2,2,2)),
                "T4R - T4R (1,2,2,2)");
  test_for_zero(t4R_3(2,0,0,0) - (t4R_1(2,0,0,0)-t4R_2(2,0,0,0)),
                "T4R - T4R (2,0,0,0)");
  test_for_zero(t4R_3(2,0,0,1) - (t4R_1(2,0,0,1)-t4R_2(2,0,0,1)),
                "T4R - T4R (2,0,0,1)");
  test_for_zero(t4R_3(2,0,0,2) - (t4R_1(2,0,0,2)-t4R_2(2,0,0,2)),
                "T4R - T4R (2,0,0,2)");
  test_for_zero(t4R_3(2,0,1,0) - (t4R_1(2,0,1,0)-t4R_2(2,0,1,0)),
                "T4R - T4R (2,0,1,0)");
  test_for_zero(t4R_3(2,0,1,1) - (t4R_1(2,0,1,1)-t4R_2(2,0,1,1)),
                "T4R - T4R (2,0,1,1)");
  test_for_zero(t4R_3(2,0,1,2) - (t4R_1(2,0,1,2)-t4R_2(2,0,1,2)),
                "T4R - T4R (2,0,1,2)");
  test_for_zero(t4R_3(2,0,2,0) - (t4R_1(2,0,2,0)-t4R_2(2,0,2,0)),
                "T4R - T4R (2,0,2,0)");
  test_for_zero(t4R_3(2,0,2,1) - (t4R_1(2,0,2,1)-t4R_2(2,0,2,1)),
                "T4R - T4R (2,0,2,1)");
  test_for_zero(t4R_3(2,0,2,2) - (t4R_1(2,0,2,2)-t4R_2(2,0,2,2)),
                "T4R - T4R (2,0,2,2)");
  test_for_zero(t4R_3(2,1,0,0) - (t4R_1(2,1,0,0)-t4R_2(2,1,0,0)),
                "T4R - T4R (2,1,0,0)");
  test_for_zero(t4R_3(2,1,0,1) - (t4R_1(2,1,0,1)-t4R_2(2,1,0,1)),
                "T4R - T4R (2,1,0,1)");
  test_for_zero(t4R_3(2,1,0,2) - (t4R_1(2,1,0,2)-t4R_2(2,1,0,2)),
                "T4R - T4R (2,1,0,2)");
  test_for_zero(t4R_3(2,1,1,0) - (t4R_1(2,1,1,0)-t4R_2(2,1,1,0)),
                "T4R - T4R (2,1,1,0)");
  test_for_zero(t4R_3(2,1,1,1) - (t4R_1(2,1,1,1)-t4R_2(2,1,1,1)),
                "T4R - T4R (2,1,1,1)");
  test_for_zero(t4R_3(2,1,1,2) - (t4R_1(2,1,1,2)-t4R_2(2,1,1,2)),
                "T4R - T4R (2,1,1,2)");
  test_for_zero(t4R_3(2,1,2,0) - (t4R_1(2,1,2,0)-t4R_2(2,1,2,0)),
                "T4R - T4R (2,1,2,0)");
  test_for_zero(t4R_3(2,1,2,1) - (t4R_1(2,1,2,1)-t4R_2(2,1,2,1)),
                "T4R - T4R (2,1,2,1)");
  test_for_zero(t4R_3(2,1,2,2) - (t4R_1(2,1,2,2)-t4R_2(2,1,2,2)),
                "T4R - T4R (2,1,2,2)");
  test_for_zero(t4R_3(2,2,0,0) - (t4R_1(2,2,0,0)-t4R_2(2,2,0,0)),
                "T4R - T4R (2,2,0,0)");
  test_for_zero(t4R_3(2,2,0,1) - (t4R_1(2,2,0,1)-t4R_2(2,2,0,1)),
                "T4R - T4R (2,2,0,1)");
  test_for_zero(t4R_3(2,2,0,2) - (t4R_1(2,2,0,2)-t4R_2(2,2,0,2)),
                "T4R - T4R (2,2,0,2)");
  test_for_zero(t4R_3(2,2,1,0) - (t4R_1(2,2,1,0)-t4R_2(2,2,1,0)),
                "T4R - T4R (2,2,1,0)");
  test_for_zero(t4R_3(2,2,1,1) - (t4R_1(2,2,1,1)-t4R_2(2,2,1,1)),
                "T4R - T4R (2,2,1,1)");
  test_for_zero(t4R_3(2,2,1,2) - (t4R_1(2,2,1,2)-t4R_2(2,2,1,2)),
                "T4R - T4R (2,2,1,2)");
  test_for_zero(t4R_3(2,2,2,0) - (t4R_1(2,2,2,0)-t4R_2(2,2,2,0)),
                "T4R - T4R (2,2,2,0)");
  test_for_zero(t4R_3(2,2,2,1) - (t4R_1(2,2,2,1)-t4R_2(2,2,2,1)),
                "T4R - T4R (2,2,2,1)");
  test_for_zero(t4R_3(2,2,2,2) - (t4R_1(2,2,2,2)-t4R_2(2,2,2,2)),
                "T4R - T4R (2,2,2,2)");

//   t3as_1(i,j,k)=t4R_1(i,j,k,l)*t1_2(l);
//   t3as_1(i,j,k)=t1_2(l)*t4R_1(i,j,k,l);
//   t3as_1(i,j,k)=t4R_1(i,j,l,k)*t1_2(l);
//   t3as_1(i,j,k)=t1_2(l)*t4R_1(i,j,l,k);
//   t3as_1(i,j,k)=t4R_1(i,l,j,k)*t1_2(l);
//   t3as_1(i,j,k)=t1_2(l)*t4R_1(i,l,j,k);
//   t3as_1(i,j,k)=t4R_1(l,i,j,k)*t1_2(l);
//   t3as_1(i,j,k)=t1_2(l)*t4R_1(l,i,j,k);

//   cout << '\n';

//   test_for_zero(t4R_1(i,j,k,l)*t4ddg_2(i,j,k,l)
//       ); test_for_zero(t4ddg_2(i,j,k,l)*t4R_1(i,j,k,l)
//       ); test_for_zero(t4R_1(i,j,k,l)*t4ddg_2(i,k,j,l)
//       ); test_for_zero(t4ddg_2(i,k,j,l)*t4R_1(i,j,k,l)
//       ); test_for_zero(t4R_3(i,j,k,l)*t4ddg_2(i,j,k,l)
//       ); test_for_zero(t4ddg_2(i,j,k,l)*t4R_3(i,j,k,l)
//       ); test_for_zero(t4R_3(i,j,k,l)*t4ddg_2(i,k,j,l)
//       ); test_for_zero(t4ddg_2(i,k,j,l)*t4R_3(i,j,k,l));

//   cout << '\n';

//   t2s_1(j,l)=t4R_1(i,j,k,l)*t2s_2(i,k);
//   t2s_1(j,l)=t2s_2(i,k)*t4R_1(i,j,k,l);
}
